Extraordinarily little is known about the organization of quantitative concepts in the young child's brain. In just six years'time (between the ages of 2 and 8 years), children traverse a complex series of learning "stages" to acquire the meanings of verbal counting words, Arabic numerals, written number words, and the procedures of basic arithmetic operations such as addition and subtraction. Researchers in the fields of psychology and education have determined that these early mathematical milestones influence children's abilities to learn mathematics for the remainder of their formal education. However, there is considerable debate over which aspects of early numerical and mathematical learning influence children's subsequent understanding of mathematics. Some researchers hypothesize that domain-general aspects of cognition provide the critical link between early and late mathematics learning whereas other researchers argue that early-developing domain-specific properties of numerical understanding such as number encoding and comparison permanently impact mathematical understanding throughout development. Neuroimaging methods offer a means for bringing new data to bear on this debate, by providing a tool with which to examine associations and dissociations among the underlying processes of numerical cognition. Such data will offer a window into the organization of mathematical information in the young child's brain and will provide novel insights into the sources, functions, and specificity of mathematical processes in the developing brain. The current proposal aims to test children (4- to 8-year-olds) and adults in functional magnetic resonance imaging (fMRI) and behavioral studies that examine the mechanisms of symbolic and nonsymbolic numerical representation and comparison, as well as the relationship between those mechanisms and performance on standardized tests. The study paradigms are designed to examine associations and dissociations among 1) symbolic and nonsymbolic numerical representation, 2) numerical encoding, comparison, and response selection, and 3) numerical quantities and non-numerical quantities such as size and space. Moreover, the proposed studies aim to test the relationships between number-specific brain responses versus domain-general brain responses and children's performance on standardized mathematics, IQ, and working memory tests. The results of these studies will reveal which number-related abilities are bound over development, how those abilities are organized in the brain during early childhood, and how number- related and domain-general brain responses are related to children's performance on different types of standardized tests. More broadly, these studies will build on the vast amount of behavioral data from children's early mathematical performance by providing new (biological) insights into the early markers of numerical and mathematical learning and will illuminate the potential bases of disorders in mathematical performance. PUBLIC HEALTH RELEVANCE: The mathematics abilities that children possess at a young age (even in preschool) affect their ability to learn math for the rest of their life. Brain imaging studies of math in young children are important for understanding what causes math abilities to develop normally and what causes them to be impaired. The results of these studies will be important for understanding poor math performance in school as well as developmental disorders that cause severe mathematical impairments.